We present a model independent approach for the reconstruction of the atomic concentration profile in a nanoscale layered structure, as measured using the X-ray fluorescence yield modulated by an X-ray standing wave (XSW). The approach is based on the direct regularized solution of the system of linear equations that characterizes the fluorescence yield. The suggested technique was optimized for, but not limited to, the analysis of periodic layered structures where the XSW is formed under Bragg conditions. The developed approach was applied to the reconstruction of the atomic concentration profiles for LaN/BN multilayers with 50 periods of 35 °A thick layers. The object is especially difficult to analyse with traditional methods, as the estimated thickness of the interface region between the constituent materials is comparable to the individual layer thicknesses. However, using the suggested technique it was possible to reconstruct the La atomic profile, showing that the La atoms stay localized within the LaN layers and interfaces and do not diffuse into the BN layer. The atomic distributions were found with an accuracy of 1 °A. The analysis of the Kr fluorescence yield showed that Kr atoms originating from the sputter gas are trapped in both the LaN-on-BN and the BN-on-LaN interfaces.